基于NURBS曲面的五轴联动插补算法

Five-axis Interpolation Algorithm Base on NURBS Surface

文章提出了一种基于NURBS曲面的五轴联动插补算法。对于NURBS曲面,确定一个参数方向的一系列参数值,就可确定一系列的另一个参数方向的NURBS曲线。沿这些曲线逐条进行插补,就可实现对整个曲面的插补。在每个插补点,求出两个参数方向的切矢,确定出该点的曲面法矢,在假设刀控方向垂直于插补曲面的情况下求出两个旋转轴的运动,实现五轴联动插补。同时,利用NURBS曲线的局部性质来保证插补的实时性。

This paper presents a interpolation algorithm based on NURBS（Non-Uniform Rational B Spline）, For NURBS surface, when a series of values of one of the two parameters are fixed, a series of NURBS curves in the other parameter direction will be obtained. Interpolating along these curves, the interpolation on the whole surface will be fulfilled. In each interpolation point, the two parameter directions Tangent Vector are found and then the Normal Vector is obtained. In terms of the Normal Vector, two angular axes movement are found and so the five-axis linkage interpolation is completed.